The Formation of Images
Suppose we want to apply some of the properties of
light discussed in the last session?
Recall the refraction of light through a prism?
Let's only consider monochromatic light for now.
Let's put a couple of
prisms together and
bring the beams of
light to a point…
If we smooth the rough edges, we can form a lens
Parallel light rays are focused into a point by the lens.
Parallel light from a distant star
• Simple Lenses are characterized by
– Focal length
– Index of refraction of the material
• This relates to how much they will bend the
A Convex Lens concentrates light
A Concave Lens spreads out light
The inverse of the focal length, measured in meters, is
For example, a +2 diopter prescription lens has a focal
length of ½ meter.
Positive is convex; Negative is concave.
The eye itself has a refractive power of 60 diopters.
This image is:
Increasing the focal length, increases the size of the image
Old Focal Point
New Focal Point
• Mirrors, using reflection instead of
refraction, also form images
The image is:
The image is…
Mirrors versus Lenses
• Mirrors have several advantages over
– Generally they are lighter in weight
– There is no problems with color
• Refraction affects different colored light so
that a for a given lens, red light will focus at
a different point than blue light
– It is easier to produce a large diameter
mirror than a large diameter lens
There are several important considerations in choosing a
• Light Gathering Power
• Resolving Power
First some definitions:
The eyepiece magnifies the image formed by the objective
Light Gathering Power
The Diameter of the objective
determines the amount of light an
optical system can gather; It is
proportional to the area of the
For example, many amateurs have 2" telescopes;
Stockton's scope is a 16"
An object seen in Stockton's scope is
64 times brighter than through a 2"
Light Gathering Power
The resolution (or clarity)
of an image also depends on
the size of the telescope
The Andromeda galaxy seen
through a small telescope…
…and through a telescope with
a larger aperture.
As objects get farther away, it becomes harder and harder to tell
them apart. Your eye cannot see all of the craters on the moon – they
blend together into the background.
In fact the circular shape of the telescope objective produces a
circular diffraction pattern as an image.
[Actually so does the circular pupil of your eye and the two straight
edges of your eyelids]
The central disk of this diffraction pattern is what we think of as the
"star" when we look at it; it is known as the Airy Disk.
It is smeared out – so, two close stars could have their Airy disks
A telescope's Resolving power measures how close together objects
can be and still be seen to be separate.
Resolving Power is measured in terms of the angular
Image #3 is "just resolved. The angle of separation when
Images are just resolved is the Resolving Power
Resolving Power =
Notice it depends on both the wavelength and the
diameter of the objective. Small numbers are 'good',
so redder light (longer wavelengths) are harder to
resolve than bluer light. The bigger the objective,
the better the resolving power.
A Rule of Thumb: ArcSec = 10/D, where D is in cm.
Resolving power in arcsec for a given objective diameter
In order to subtend the same angle with a dime, you
would to be these many miles away:
Twinkle, Twinkle Little Star…
Because the light from the star
follows a winding path through
the (sometimes turbulent)
atmosphere, the star appears
to move around a bit.
The motion varies between 1"
and 2" (best case is 0.25")
What angles do the planets subtend?
This means that the movement (twinkle) is smaller than
the planet – so any motion is invisible; the motion is
within the bounds of the planet. This leads to a rule:
Magnification is the least important of the telescope
properties (although the one touted by TV sales shows).
Unless you are looking only at planets, the moon or other
extended objects, magnifying the point of light that is a star
Magnification is the ration of the focal lengths of the objective
and the eyepiece:
The Stockton 16" has a focal length of 4064 mm
32mm eyepiece M = 4064/32 = 127x
24mm eyepiece M = 4064/24 = 170x
A telescope mount has two functions
provide a system for smooth controlled movement to
point and guide the instrument
2. support the telescope firmly so that you can view and
photograph objects without having the image disturbed
There are two major types of mounts for
• The simplest type of mount with two
motions, altitude (up and down/vertical)
and azimuth (side-to-side/horizontal).
• Good altazimuth mounts will have slowmotion knobs to make precise
adjustments, which aid in keeping
tracking motion smooth.
• These type mounts are good for
terrestrial observing and for scanning
the sky at lower power, but are not for
deep sky photography.
• Certain altazimuth mounts are now
computer driven and allow a telescope
to track the sky accurately enough for
visual use, but not for long exposure
• Superior to non-computerized altazimuth mounts for astronomical
observing over long periods of time and absolutely necessary for
• As the earth rotates around its axis, the stationary stars appear to
move across the sky. If you are observing them using an altazimuth
mount, they will quickly float out of view in both axes.
• A telescope on an equatorial mount can be aimed at a celestial
object and easily guided either by manual slow-motion controls or by
an electric clock drive to follow the object easily across the sky and
keep it in the view of the telescope.
• The equatorial mount is rotated on one axis (polar/right ascension)
adjusted to your latitude and that axis is aligned to make it parallel to
the Earth's axis, so that if that axis is turned at the same rate of
speed as the Earth, but in the opposite direction, objects will appear
to sit still when viewed through the telescope.
Both reflector and refractor
telescopes normally use
this type mount.
A large counterweight
extending on the opposite
side of the optical tube is
its distinguishing feature.
The counterweight is
needed to balance the
weight of the optical tube.
Most catadioptric and other shorter
optical tubes use this style
mount which is generally more
convenient to use than the
German mount, especially for
A more recent state-of-the-art
computer controlled telescope
allows fully automatic operation
making it easy to locate objects
while saving the observer
considerable time and effort.
Types of Telescopes
Refractor versus Reflector
The 'classic' telescope most of us think of when we
imagine one is the refractor. In practice,
however, there are some significant drawbacks
to refractors – especially those of large size.
As usual, the telescope is measured by its objective
diameter. The largest refractor is 40".
Refractors suffer from two main problems
1. Chromatic Aberration
Recall that refraction bends light differently depending
on its wavelength. This means that different colors will
have differing focal lengths:
Resulting in an image with "color halos"
Generally, the bigger the objective
diameter, the longer the focal length
and therefore the higher in the air
the lens of the refractor will be when
mounted in the telescope tube.
Since large refractors could have an
objective lens weighing in the tons,
moving it about is a definite problem.
• Reflectors on the other hand have no
chromatic aberration - reflection acts the
same no matter what the wavelength of the
• Second, mirrors are generally placed closer
to the ground and with a lower center of
gravity are easier to move.
• Mirrors are usually spherical rather than
parabolic – leading to spherical aberation
(because it's cheaper & easier to make a spherical mirror)
The world’s largest
One property of a parabolic shape is the fact that any
incoming parallel rays will be focused to a single point:
A spherical shape does not have this property:
Types of Reflectors
Types of Reflectors: Prime Focus
Observer rides in a
'basket' inside the
Yes, it blocks some light.
No, it doesn't change the
image, just dims it a bit
at Kitt Peak National
Types of Reflectors: Herschell
The eyepiece is set at the top of
the tube and the mirror
canted so that the light will be
focused into the eyepiece
Drawback: You might be very far
off the ground on a ladder
trying to see some objects –
this is especially thrilling when
trying to move the scope to
follow the motion of a planet
"This wonderful instrument, though gigantic in its size, is moved with great
facility in all directions, by means of rollers, ropes, and pullies. The ascent to
the uppermost end is by means of steps or rather a ladder; and to this end
there is a seat attached, on which the astronomer is placed to make his
observations on the starry world. Of course he looks in, and not through the
tube; in the lower end of which, near the ground, is placed the mirror which
reflects the light through a small tube, upon his eyes. The mirror weighs two
thousand five hundred pounds, and is worth, according to the doctor's
valuation, ten thousand pounds.
While he views the firmament with its glittering orbs, he communicates his
observations to his sister, Miss Herschell, who is his amanuensis, and who has
her station in a small lodge built in the lower framework of the machinery.
This he does by a speaking trumpet, one end of which is applied to his mouth,
and the other to her ear; thus they are recorded without either having to
leave their seats…"
--Description of Herschell's telescope at Slough from Joshua White's
Letters on England, written in 1810.
Types of Reflectors: Newtonian
A Newtonian reflector allows you
to "keep your feet on the
It does this by placing a diagonal
mirror in the tube so that the
eyepiece may be lower.
The small amount of light blocked
by the mirror is minimal in return
for the convenience and
usefulness of the lower placement
of the eyepiece
Types of Reflectors: Cassegrain
This clever arrangement puts a
small convex mirror in front of
the objective and bores a hole in
The small mirror reflects the
incoming light through the hole
and into the eyepiece. This
arrangement allows the focal
length to be increased dependent
on the placement of the small
Types of Reflectors: Coudé
Suppose you want to put a camera, or
even heavier equipment, in line with
the telescope optics.
Even the cassegrain focus can be hardpressed to handle several hundred
pounds of analysis equipment hanging
on the back of the scope.
The arrangement makes use of the fork
method of the equatorial mount. Light
can be directed into the point where
the scope tube is gripped by the fork
and then directed down through the
mounting (conveniently hollow or with
fiber optics) to a room below the
telescope where the equipment is
Types of Reflectors: Schmidt
Sometimes called a Schmidt
Camera, this design allows the
use of a spherical mirror and a
These usually have wide fields of
vision and "fast optics" allowing
Many of these are also Cassegrain
– leading to the designation
– Cameras and film
– Photoelectric photometers
– Charge-Coupled Devices (CCD)
Instruments and Detectors
Instead of using
photographic plates to take
pictures, we use sensitive
solid-state light detectors
known as Charge Coupled
CCDs can detect light with
an efficiency of greater
Instruments and Detectors
Comparison between a photographic plate and a CCD
image with the same amount of exposure. The CCD is
much more sensitive to light!
• Radio Telescopes
A radio telescope in Australia.
The Very Large Array (VLA) in
New Mexico is the world’s best
The largest telescope
in the world is the
1000-ft diameter radio
telescope of the
in Puerto Rico.
Gamma Ray Observatories
Chandra Space Telescope
The Chandra X-ray Observatory
Observations of the supernova remnant, IC 443
The close-up, shows a neutron star that is spewing
out a comet-like wake of high-energy particles
Hubble Space Telescope
By observing objects at different wavelengths we learn different
things. This is the Whirlpool Galaxy (Messier 51) observed in:
Slides adapted from Dr Claire Max, UCSC
Why is adaptive optics needed?
Turbulence in earth’s
atmosphere makes stars twinkle
More importantly, turbulence
spreads out light; makes it a
blob rather than a point
Images of a bright star, Arcturus
Lick Observatory, 1 m telescope
Turbulence arises in several places
wind flow over dome
~ 1 km
Heat sources w/in dome
If there’s no close-by “real”
star, create one with a laser
Use a laser beam
at altitude of
100 km in
Laser is operating at Lick Observatory,
being commissioned at Keck
Galactic Center with Keck laser guide star
Keck laser guide star AO
Best natural guide star AO
Adaptive optics makes it possible to find
faint companions around bright stars
Two images from Palomar of a brown dwarf
companion to GL 105
Credit: David Golimowski
The new generation:
adaptive optics on 8-10 m telescopes
Summit of Mauna Kea volcano in Hawaii:
Neptune in infra-red light
2.3 arc sec
Without adaptive optics
May 24, 1999
June 27, 1999
Neptune at 1.6 m: Keck AO exceeds
resolution of Hubble Space Telescope
HST - NICMOS
~2 arc sec
2.4 meter telescope
10 meter telescope
(Two different dates and times)
Uranus with Hubble Space Telescope
and Keck AO
Keck AO, IR
VLT NAOS AO first light
Cluster NGC 3603: IR AO on 8m ground-based telescope
achieves same resolution as HST at 1/3 the wavelength
Hubble Space Telescope
WFPC2, = 800 nm
NAOS AO on VLT
= 2.3 microns
The National Observatories:
Cerro Tololo Inter-American
Observatory, Chilean Andes
Kitt Peak National
For several reasons, most observatories
are built on top of high mountains in
remote areas of the world.
This image shows the summit of Mauna
Kea, at an altitude of 14,000 ft.
The twin 10-meter Keck reflecting telescopes on Mauna
Kea, Hawaii, are the world’s largest.
consist of 36
create the 10meter reflecting
The Gemini 8-m telescopes:
Gemini South, Chile
Gemini North, Mauna Kea
The Very Large Telescope(s): Four 8-m telescopes
To Infinity, and Beyond!
Dawn is a space probe launched by NASA in
2007 to study the two most-massive
objects of the asteroid belt: the
protoplanet Vesta and the dwarf planet
Currently enroute to Ceres, it is expected
to arrive March 6, 2015
Cassini launched in October 1997 with the European Space Agency's Huygens probe. The probe was
equipped with six instruments to study Titan, Saturn's largest moon. It landed on Titan's surface on
Jan. 14, 2005, and returned spectacular results.
Meanwhile, Cassini's 12 instruments have returned a daily stream of data from Saturn's system
since arriving at Saturn in 2004.
Cassini completed its initial four-year mission to explore the Saturn System in June 2008 and the
first extended mission, called the Cassini Equinox Mission, in September 2010. Now, the healthy
spacecraft is seeking to make exciting new discoveries in a second extended mission called the
Cassini Solstice Mission. The mission’s extension, which goes through September 2017, is named for
the Saturnian summer solstice occurring in May 2017.
Earth as seen by Cassini at Saturn
The fastest spacecraft when it was launched, New Horizons lifted off in January 2006.
It awoke from its final hibernation period last month after a voyage of more than 3 billion miles, and
will soon pass close to Pluto, inside the orbits of its five known moons.
The spacecraft is entering the first of several approach phases that culminate July 14 with the first
close-up flyby of the dwarf planet, 4.67 billion miles (7.5 billion kilometers) from Earth.
On August 3, 2004, NASA’s MESSENGER spacecraft blasted off from Cape Canaveral,
Florida, for a risky mission that would take the small satellite dangerously close to
Mercury’s surface, paving the way for an ambitious study of the planet closest to the
The spacecraft traveled 4.9 billion miles (7.9 billion kilometers) — a journey that
included 15 trips around the Sun and flybys of Earth once, Venus twice, and Mercury
three times — before it was inserted into orbit around its target planet in 2011.